Sudoku Disjoint Chain Method

The "Disjoint Chain" method is a more advanced method that can be used when other methods cannot solve the puzzle. This may be required for the hard difficulty puzzles. This method is also known as the Naked Triples or Hidden Triples method.

Look at the green squares in this first example. Notice how the numbers 1, 2 and 3 are the only candidates for these cells. This is called a chain. Since the numbers 1, 2 and 3 must appear in these three cells, they cannot appear in any other cells in this sub-square. In particular, we can remove the numbers 1 and 3 from the red cells.

This second example is essentially the same as the first. It has just been rearranged a little bit to demonstrate that the chain can appear in a row or column just as easily as it can appear in a sub-square.

Additionally, you could have a chain of 4 or more cells, although these are generally difficult to identify.